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Temperature and pressure couplingPowerPoint Presentation

Temperature and pressure coupling

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Why control the temperature and pressure?

- isothermal and isobaric simulations (NPT) are most relevant to experimental data
- constant NPT ensemble: constant number of particles, pressure, and temperature

Causes of temperature and pressure fluctuations

the temperature and pressure of a system tends to drift due to several factors:

- drift as a result of integration errors
- drift during equilibration
- heating due to frictional forces
- heating due to external forces

Temperature coupling methods in GROMACS

weak coupling

- exponential relaxation Berendsen temperature coupling (Berendsen, 1984)
extended system coupling

- oscillatory relaxation Nosé-Hoover temperature coupling (Nosé, 1984; Hoover, 1985)

Berendsen temperature coupling

- there is weak coupling to an external ‘heat bath’
- deviation of system from a reference temperature To is corrected
- exponential decay of temperature deviation

- the temperature of a system is related to its kinetic energy, therefore, the temperature can be easily altered by scaling the velocities vi by a factor λ
- is the temperature coupling time constant
- need to specify in input file (*.mdp file)

Some notes on Berendsen weak coupling algorithm energy, therefore, the temperature can be easily altered by scaling the velocities v

- very efficient for relaxing a system to the target temperature
- prolonged temperature differences of the separate components leads to a phenomenon called ‘hot-solvent, cold-solute’, even though the overall temperature is at the correct value
Solutions:

- apply temperature coupling separately to the solute and to the solvent problem with unequal distribution of energy between the different components

solutions energy, therefore, the temperature can be easily altered by scaling the velocities vcontinued …

- stochastic collisions (Anderson, 1980)
- a random particle’s velocity is reassigned by random selection from the Maxwell-Boltzmann distribution at set intervals does not generate a smooth trajectory, less realistic dynamics

- extended system (Nosé, 1984; Hoover 1985)
- the thermal reservoir is considered an integral part of the system and it is represented by an additional degree of freedom s

- used in GROMACS

Nos energy, therefore, the temperature can be easily altered by scaling the velocities vé-Hoover extended system

- canonical ensemble (NVT)
- more gentle than Anderson where particles suddenly gain new random velocities
- the Hamiltonian is extended by including a thermal reservoir term s and a friction parameter ξ, in the equations of motion
H = K + V + Ks + Vs

Nos energy, therefore, the temperature can be easily altered by scaling the velocities vé-Hoover extended system

- The particles’ equation of motion:
- ξ is a dynamic quantity with its own equation of motion:
- is proportional to the temperature coupling time constant (specified in *.mdp file)

- the strength of coupling between the reservoir and the system is determined by
- when is too high slow energy flow between system and reservoir

- when is too low rapid temperature fluctuations

- Nos system is determined by é-Hoover produces an oscillatory relaxation, it takes several times longer to relax with Nosé-Hoover coupling than with weak coupling
- can use Berendsen weak coupling for equilibration to reach desired target, then switch to Nosé-Hoover
- Nosé-Hoover chain: the Nose-Hoover thermostat is coupled to another thermostat or a chain of thermostats and each are allowed to fluctuate

Pressure coupling system is determined by

- The system can be coupled to a ‘pressure bath’ as in temperature coupling
weak coupling:

exponential relaxation Berendsen pressure coupling

extended ensemble coupling:

oscillatory relaxation Parrinello-Rahman pressure coupling (Parrinello and Rahman, 1980, 1981, 1982)

Berendsen pressure coupling system is determined by

- equations of motion are modified with a
first order relaxation of P towards a reference Po

- rescaling the edges and the atomic coordinates ri at each step by a factor u leads to volume change
- u is proportional to β which is the isothermal compressibility of the system and which is the pressure coupling time constant. Both values must be specified in *.mdp file

- Berendsen scaling can be done: system is determined by
1. isotropically – scaling factor is equal for all three directions i.e. in water

2. semi-isotropically where the x/y directions are scaled independently from the z direction i.e. lipid bilayer

3. anisotropically – scaling factor is calculated independently for each of the three axes

Parrinello-Rahman pressure coupling system is determined by

- volume and shape are allowed to fluctuate
- extra degree of freedom added, similar to Nosé-Hoover temperature coupling, the Hamiltonian is extended
box vectors and W-1 are functions of M

- W-1determines the strength of coupling
have to provide βand

in the input file (*.mdp file)

- if your system is far from equilibrium, it may be best to use weak coupling (Berendsen) to reach target pressure and then switch to Parrinello-Rahman as in temperature coupling
- in most cases the Parrinello-Rahman barostat is combined with the Nosé-Hoover thermostat
- the extended methods are more difficult to program but safer

Weak coupling in *.mdp file use weak coupling (Berendsen) to reach target pressure and then switch to Parrinello-Rahman as in temperature coupling

; OPTIONS FOR WEAK COUPLING ALGORITHMS =

; Temperature coupling =

tcoupl = berendsen

; Groups to couple separately =

tc-grps = Protein SOL_Na

; Time constant (ps) and reference temperature (K) =

tau-t = 0.1 0.1

ref-t = 300 300

; Pressure coupling

Pcoupl = berendsen

Pcoupltype = isotropic

; Time constant (ps), compressibility (1/bar) and reference P (bar) =

tau-p = 1.0

compressibility = 4.5E-5

ref-p = 1.0

Extended system coupling in *.mdp file use weak coupling (Berendsen) to reach target pressure and then switch to Parrinello-Rahman as in temperature coupling

; OPTIONS FOR WEAK COUPLING ALGORITHMS =

; Temperature coupling =

tcoupl = nose-hoover

; Groups to couple separately =

tc-grps = PROTEIN SOL_Na

; Time constant (ps) and reference temperature (K) =

tau-t = 0.5 0.5

ref-t = 300 300

; Pressure coupling =

Pcoupl = parrinello-rahman

Pcoupltype = isotropic

; Time constant (ps), compressibility (1/bar) and reference P (bar) =

tau-p = 5.0

compressibility = 4.5E-5

ref-p = 1.0

References use weak coupling (Berendsen) to reach target pressure and then switch to Parrinello-Rahman as in temperature coupling

- Berendsen, H.J.C., Postma, J.P.M., DiNola, A., Haak, J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys.81:3684-3690, 1984
- Nosé, S. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52:255-268, 1984
- Hoover, W.G. Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A31:1695-1697, 1985
- Berendsen, H.J.C. Transport properties computed by linear response through weak coupling to a bath. In: Computer Simulations in Material Science. Meyer, M., Pontikis, V. eds. Kluwer 1991, 139-155
- Parrinello, M., Rahman, A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 52:7182-7190, 1981
- Nosé, S., Klein, M.L. Constant pressure molecular dynamics for molecular systems. Mol. Phys. 50: 1055-1076, 1983

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